Geodesics and Deformed Pseudo-Riemannian Manifolds with Symmetry

James J. Hebda

Abstract: There is a general method, applicable in many situations, whereby a pseudo-Riemannian metric, invariant under the action of some Lie group, can be deformed to obtain a new metric whose geodesics can be expressed in terms of the geodesics of the old metric and the action of the Lie group. This method applied to Euclidean space and the unit sphere produces new examples of complete Riemannian metrics whose geodesics are expressible in terms of elementary functions.